In a multicarrier system, a communication path having a fixed bandwidth is divided into a number of sub-bands having different frequencies. The width of the sub-bands is chosen to be small enough to allow the distortion in each sub-band to be modeled by a single attenuation and phase shift for the band. If the noise level in each band is known, the volume of data sent in each band may be optimized by choosing a symbol set having the maximum number of symbols consistent with the available signal-to-noise ratio of the channel. By using each sub-band at its maximum capacity, the amount of data that can be transmitted in the communication path is maximized.
In practice, such systems are implemented by banks of digital filters which make use of fast Fourier transforms or other transforms as described in detail below. Consider the case in which a single data stream is to be transmitted over the communication path which is broken into M sub-bands. During each communication cycle, the portion of the data stream to be transmitted is converted to M symbols chosen to match the capacity of the various channels. Each symbol is the amplitude of a corresponding sub-carrier. The time domain signal to be sent on the communication path is obtained by modulating each sub-carrier by its corresponding amplitude and then adding the modulated carriers to form the signal to be placed in the communication path. This operation is normally carried out by transforming the vector of M symbols via the inverse Fourier transform to generate M time domain values that are sent in sequence on the communication path. At the other end of the communication path, the M time domain values are accumulated and transformed via a Fourier transform to recover the original M symbols after equalization of the transformed data to correct for the attenuation and phase shifts that occurred in the channels.
The above discussion assumes that the time domain signal is sent on the communication path in the base band. For many applications, it is desirable to upconvert the multichannel signal at the transmitter so that it is sent in a higher frequency band. This is accomplished by modulating a high frequency carrier with the multicarrier signal. To minimize the bandwidth of the data about the high frequency carrier, it is advantageous to use single side band modulation of the carrier. A single side band upconversion of a signal s(t) to frequency f may be generated from s(t) and s(t), where s(t) is the Hilbert transform of s(t), according to the formula EQU F(t)=s(t)*cos(2.pi.ft)+s(t) sin(2.pi.ft) (1)
The pair of signals, s(t) and s(t), are also known as an in-phase and quadrature pair of signals.
The computational workload imposed by the need to generate the Hilbert transform of s(t) from s(t) is a significant. This is often accomplished with an FIR filter which, depending on the design goals, requires many tens or hundreds of taps. It can also be accomplished using analog bandpass filters, but satisfactory analog designs are difficult to manufacture to the required accuracy.
Broadly, it is the object of the present invention to provide an improved multi-carrier transmission system.
It is a further object of the present invention to provide a multi-carrier transmission system that provides both the in-phase and quadrature components needed to generate a single side-band modulation of a high frequency carrier with a computational workload that is significantly less than that required to generate the components by directly computing the Hilbert transform of s(t).
These and other objects of the present invention will become apparent to those skilled in the art from the following detailed description of the invention and the accompanying drawings.